Authors: Richard Ehrenborg ¹; Sergey Kitaev ²; Einar Steingrımsson

• 1 Department of Mathematics
• 2 Department of Computer and Information Sciences [Univ Strathclyde]

The graph of overlapping permutations is defined in a way analogous to the De Bruijn graph on strings of symbols. However, instead of requiring the tail of one permutation to equal the head of another for them to be connected by an edge, we require that the head and tail in question have their letters appear in the same order of size. We give a formula for the number of cycles of length $d$ in the subgraph of overlapping $312$-avoiding permutations. Using this we also give a refinement of the enumeration of $312$-avoiding affine permutations.